Question: Simplify the following expression: $ t = \dfrac{-5p + 7}{-7p} + \dfrac{-9}{4} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-5p + 7}{-7p} \times \dfrac{4}{4} = \dfrac{-20p + 28}{-28p} $ Multiply the second expression by $\dfrac{-7p}{-7p}$ $ \dfrac{-9}{4} \times \dfrac{-7p}{-7p} = \dfrac{63p}{-28p} $ Therefore $ t = \dfrac{-20p + 28}{-28p} + \dfrac{63p}{-28p} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-20p + 28 + 63p}{-28p} $ $t = \dfrac{43p + 28}{-28p}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{-43p - 28}{28p}$